Supercomputers are the fastest and the most expensive computers. These huge computers are used to solve very complex science and engineering problems. Supercomputers get their processing power by taking advantage of parallel processing; they use lots of CPUs at the same time on one problem. A typical supercomputer can do up to ten trillion individual calculations every second.
Example Supercomputers:

Servers are a step under supercomputers, because they don't focus on trying to solve one very complex problem, but try to solve many many similar smaller ones.
An example of servers would be the computers that Wikipedia stores its encyclopedia on. Those computers have to go and find the page you're looking for and send it to you. In itself it's not a big task, but it becomes a job for a server when the computers have to go and find lots of pages for a lot of people and send them to the right place. Some servers, like the ones Google uses for something like Google Documents, have applications on them instead of just files, like Wikipedia.

A server is a central computer that contains collections of data and programs.
Also called a network server, this system allows all connected users to share and store electronic data and applications.
Two important types of servers are file servers and application servers.

Workstations are high-end, expensive computers that are made for more complex procedures and are intended for one user at a time. Some of the complex procedures consist of science, math and engineering calculations and are useful for computer design and manufacturing. Workstations are sometimes improperly named for marketing reasons. Real workstations are not usually sold in retail, but this is starting to change; Apple's Mac Pro would be considered a workstation.

PC is an abbreviation for a Personal Computer, it is also known as a Microcomputer. Its physical characteristics and low cost are appealing and useful for its users. The capabilities of a personal computer have changed greatly since the introduction of electronic computers. By the early 1970s, people in academic or research institutions had the opportunity for single-person use of a computer system in interactive mode for extended durations, although these systems would still have been too expensive to be owned by a single individual. The introduction of the microprocessor, a single chip with all the circuitry that formerly occupied large cabinets, led to the proliferation of personal computers after about 1975. Early personal computers, generally called microcomputers, sold often in kit form and in limited volumes and were of interest mostly to hobbyists and technicians. By the late 1970s, mass-market pre-assembled computers allowed a wider range of people to use computers, focusing more on software applications and less on development of the processor hardware. Throughout the 1970s and 1980s, home computers were developed for household use, offering some personal productivity, programming and games, while somewhat larger and more expensive systems (although still low-cost compared with minicomputers and mainframes) were aimed for office and small business use.

Today a personal computer is an all-around device that can be used as a productivity tool, a media server and a gaming machine. The modular construction of the personal computer allows components to be easily swapped out when broken or upgrading.

Microcontrollers are mini computers that enable the user to store data and execute simple commands and tasks. These single circuit devices have minimal memory and program length but are normally designed to be very good at performing a niche task. Many such systems are known as embedded systems. The computer in your car, for example is an embedded system. A common microcontroller that one might come across is called Arduino.

Do you own a smartphone? Your smart phone is a computer! Most smartphones run iOS or Android. Android is an operating system that is based on Linux. Smartphones are becoming exponentially faster and also have an exponentially increasing data capacity.